论文标题
伪图形卷积网络：针对大型图形和超图量的快速过滤器
Pseudoinverse Graph Convolutional Networks: Fast Filters Tailored for Large Eigengaps of Dense Graphs and Hypergraphs
论文作者
论文摘要
事实证明，图形卷积网络（GCN）已成为成功的工具，用于基于图的数据集中的半监督分类。我们提出了一种新的GCN变体，其三部分滤波器空间针对密集图。示例包括3D点云的高斯图，其重点增加了非本地信息，以及基于分类数据的超图。这些图与其图laplacian的光谱特性方面不同于常见的稀疏基准图。最值得注意的是，我们观察到大型特征，这对于流行的现有GCN体系结构不利。我们的方法通过利用Laplacian的伪源来克服这些问题。另一个关键成分是卷积矩阵的低级别近似值，确保了计算效率和同时提高精度。我们概述了如何在每个应用程序中有效地计算必要的特征性信息，并讨论唯一的元配合体近似等级的适当选择。我们最终在使用现实世界数据集的各种实验中展示了我们的方法在运行时和准确性方面的性能。
Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs. Examples include Gaussian graphs for 3D point clouds with an increased focus on non-local information, as well as hypergraphs based on categorical data. These graphs differ from the common sparse benchmark graphs in terms of the spectral properties of their graph Laplacian. Most notably we observe large eigengaps, which are unfavorable for popular existing GCN architectures. Our method overcomes these issues by utilizing the pseudoinverse of the Laplacian. Another key ingredient is a low-rank approximation of the convolutional matrix, ensuring computational efficiency and increasing accuracy at the same time. We outline how the necessary eigeninformation can be computed efficiently in each applications and discuss the appropriate choice of the only metaparameter, the approximation rank. We finally showcase our method's performance regarding runtime and accuracy in various experiments with real-world datasets.
